Optimal Delay Allocation under High Flexibility Conditions during Demand-Capacity Imbalance A theoretical approach to show the potential of the User Driven Prioritisation Process Sergio RUIZ (PJ07.2 UDPP) 28 Nov 2017 The European Organisation for the Safety of Air Navigation
Outline • Introduction, Motivation and Methodology • Recall: Cost of delay and current UDPP features • Problem of LVUCs and potential new UDPP features • Flexibility vs. Equity • Mathematical analysis and examples • Conclusions and future work 2
Introduction Profitability in air transport industry is very sensitive to cost • variations (profit margins might be as low as 1-2%). [Ref: IATA ] • DCB protects well the safety and capacity performances by applying delays in FPFS order when there is congestion at airports . However, DCB has no visibility of the impact of delay on AUs operations. AUs would like further flexibility to reduce the 'impact of delay' • (cost of delay) during irregular operations. User-driven approach could be a good solution to achieve • efficiency (while safety can be preserved) in the ATFM slot/delay allocation. [Ref: Fundamental Theorem of Welfare ]. 3
How to give flexibility to AUs while not impacting negatively to others? User-Driven Prioritisation Process ( UDPP ) is being developed in • the context of SESAR Today, UDPP allows Enhanced Slot Swapping , which gives • flexibility to some AUs with no impact to others time 2 flights 1 flight But, what about Low Volume Users in Constraint ( LVUC ), i.e., • AUs with a few flights (e.g., 3 or less) 4
Low Volume Users in Constraint (LVUCs) According to analysis of the last 20 AIRACs, in the 85% of the • hotspots the AUs have 3 flights or less (they are LVUCs) Limited flexibility in these cases About in 2/3 of the regulations the AUs will have 1 flight • operated in a hotspot No flexibility with current UDPP Some AUs are always LVUCs Problem of access • It is mandatory to give access to LVUCs in UDPP Important: any AU can be an LVUC (quite often indeed) • 5
Motivation • With this presentation we want: • To explore the limits of flexibility beyond the current UDPP validated features ( to include LVUCs ). • To know what is the dominant strategy of an AU when he can optimise his cost of delay subject to equity constraints • To show that in theory we could have a win-win situation if: • Slot exchange is allowed between AUs • Each AU tries to optimise their own cost of delay • AUs are constrained by equity rules (‘ what is taken from others must be given back at some point’ ) 6
Methodology High flexibility subject to equity will be discussed. • Via developing the User Delay Optimisation Model (UDOM) • and analysing the results and implications • Hypothetical case to study: • The AU has high/full flexibility to transfer its total baseline delay (i.e., initial ATFM delay) among his flights • For that purpose, the AU can take flight sequence positions to other AUs (freely!) • The AU is subject to a particular equity constraint: total baseline delay of the AU cannot be reduced . 7
Operational Cost of delay for Airspace Users ? From AU: No way to Act on Delay -> Act on Operational Cost of the Delay Cost of delay on 1 flight Non-linear cost structure due to : PAX flow: transit, high yield passengers, rotations,… Slope = punctuality policy Resource Mgt. (cascade): curfew, (reputation) crew constraints, pilots constraints, maintenance, ... Delay First max delay target ( Margin of manoeuvre 1 ) 2nd max delay target ( Margin of manoeuvre 2 ) Each flight has its own particular complex cost structure only known by the AU
Recall: Current UDPP UDPP Slot Swapping has demonstrated real benefits for AUs … FL001 FLXXX FLXXX FLXXX FL002 FLXXX FL003 FLXXX … … FL002 FLXXX FLXXX FLXXX FL001 FLXXX FL003 FLXXX … D2 D1 FL001 FL001 D1 D2 FL002 FL002 Current UDPP feature D3 D3 FL003 (slot re-ordering) FL003 FL002 -> FL001 FL001 -> FL002 Global cost = Global cost = In current UDPP flexibility is limited by the own number of flights in a hotspot and the re-scheduling limits(slots too far away are not feasible)
Potential new advanced UDPP features The AU cannot improve the situation with current UDPP … FL002 FLXXX FLXXX FLXXX FL001 FLXXX FL003 FLXXX … … FL002 FLXXX FLXXX FL001 FLXXX FLXXX FLXXX FL003 … D2 D2 FL001 FL001 D1 D1 FL002 FL002 UDPP potential extension D3 D3 FL003 FL003 (slot exchange among AUs) FL001 -- Delay FL003 ++Delay Global cost = Global cost = New advanced UDPP features are needed to give access to LVUCs and potentially to increase flexibility for everyone ( slot exchange between AUs )
LVUCs should have access throughout different hotspots The AU cannot improve the situation with current UDPP Hotspot 1 Hotspot 1 D1 D1 UDPP potential extension (slot exchange among AUs FL001 FL001 and in multiple hotspots) FL001 ++ Delay Hotspot 2 FL002 -- Delay Hotspot 2 D2 D2 FL002 FL002 New advanced UDPP features are needed to give access to LVUCs ( slot exchange between AUs and possibly throughout multiple hotspots )
impact to other AUs UDPP Flexibility vs Equity relationship Others? Flexibility (for cost optimisation) Accepted NI to be compensated in long term (UDPP for LVUCs) Current UDPP Accepted NI to be compensated in short term Negligible Positive Impact Negative (SFP) Impact (NI) not compensated No impact (Slot Swapping) (FDR) No UDPP Impact to others (before compensation) The higher the immediate impact to others and the longer the time for compensation, the more difficult to develop and validate an equitable UDPP method 12
Whom compensates whom? UDPP Flexibility vs Equity relationship Others? Flexibility (for cost optimisation) Accepted NI to be compensated by any AU (e.g., A gives d minutes to B, B gives d minutes to C, C gives d minutes to A) Accepted NI to be compensated directly by the same AU (e.g., A gives d minutes to B, and B pay back d minutes) Level of crossed compensations It might be more difficult to prove equity in case of crossed compensations among AUs (but more flexibility is expected). 13
USER DELAY OPTIMISATION MODEL (UDOM) 14
Description of parameters 15
UDOM: Utility of a flight Utility can be understood as the value perceived by a particular AU if a given slot is allocated to a particular flight operated (directly related with the economic profits) Different U 0 and ε to model different carriers: 2 d 2 U 0 Utility Utility U d d 0, U 0 0, 0 U 0 U 0 Continuous model (simplification) U’ 0 U’ 0 ' d (delay) d (delay) Utility = Profit – Delay Cost 16
UDOM: Utility of an AU Each AU will receive the utility of all its flights, the ones without delay and the ones with delay Sum of utilities of flights Sum of utilities of flights operated without delay operated with delay N N 1 i i U U i i U i d 0 i 1 i 1 Average delay Probability of flight i of being Delay = 0 Expected long-term expected for flight i regulated and delayed utility for the AU Probability of flight i of not being delayed 17
UDOM: Utility of an AU The average long-term utility perceived by an AU will be always below the ideal case in which there is no delay 18
UDOM: Flexibility and Equity High Flexibility : in case of a hotspot, the AU would be allowed to freely change the delay of its flights with a delay shift, τ 2 U 0 U d 2 d The delay shift is added to the baseline delay of a flight Equity: to avoid potential system abuses, the model forces an equity constraint to AUs: baseline delay cannot be reduced N i 0 i 0 The sum of delay shifts must be zero 19
UDOM: General optimisation model Under high flexible-equitable conditions an AU with N flights faces the following optimisation problem 1 i i N N 1 ,..., N U i i i max U U i d 0 i 1 i 1 N i 0 s . t . Flexibility: Delay shift for i 1 each flight Equity constraint Optimal Delay per flight: N j * j 1 i i i i N j j j 1 20
UDOM: Example 1 Example : LVUC with 3 flights in the same hotspot. 1 (hotspot is actually happening) we use actual (random) delay instead of average delay F1 Utility D1 = 5’ F1 Utility D1 = 5’ D1 = 26’ * 21 U 0 500 f 1 2 f 1 U 0 500 f 1 2 Optimised sequence d (delay) F2 Utility d (delay) D2 = 12’ F2 Utility * 7 D2 = 12’ D2 = 5’ U 0 500 f 2 10 f 2 U 0 500 f 2 10 Optimised sequence d (delay) F3 Utility d (delay) D3 = 20’ F3 Utility * 14 D3 = 11’ D3 = 20’ U 0 500 f 3 U 0 500 f 3 9 f 3 9 Optimised sequence Delay shift between flights (sum d (delay) equal to zero) 21 d (delay)
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